## Types in MathNet.Numerics.LinearAlgebra.Factorization

Type Evd<T>

Namespace MathNet.Numerics.LinearAlgebra.Factorization

Interfaces ISolver<T>

Eigenvalues and eigenvectors of a real matrix.
If A is symmetric, then A = V*D*V' where the eigenvalue matrix D is diagonal and the eigenvector matrix V is orthogonal. I.e. A = V*D*V' and V*VT=I. If A is not symmetric, then the eigenvalue matrix D is block diagonal with the real eigenvalues in 1-by-1 blocks and any complex eigenvalues, lambda + i*mu, in 2-by-2 blocks, [lambda, mu; -mu, lambda]. The columns of V represent the eigenvectors in the sense that A*V = V*D, i.e. A.Multiply(V) equals V.Multiply(D). The matrix V may be badly conditioned, or even singular, so the validity of the equation A = V*D*Inverse(V) depends upon V.Condition().

### Public Methods

#### Matrix<T>Solve(Matrix<T> input)

Solves a system of linear equations, , with A EVD factorized.
##### Parameters
###### `Matrix<T>` input

The right hand side Matrix`1 , .

##### Return
###### `Matrix<T>`

The left hand side Matrix`1 , .

#### voidSolve(Matrix<T> input, Matrix<T> result)

Solves a system of linear equations, , with A EVD factorized.
##### Parameters
###### `Matrix<T>` input

The right hand side Matrix`1 , .

###### `Matrix<T>` result

The left hand side Matrix`1 , .

#### Vector<T>Solve(Vector<T> input)

Solves a system of linear equations, , with A EVD factorized.
##### Parameters
###### `Vector<T>` input

The right hand side vector, .

##### Return
###### `Vector<T>`

The left hand side Vector`1 , .

#### voidSolve(Vector<T> input, Vector<T> result)

Solves a system of linear equations, , with A EVD factorized.
##### Parameters
###### `Vector<T>` input

The right hand side vector, .

###### `Vector<T>` result

The left hand side Matrix`1 , .

### Public Properties

#### Matrix<T>D get;

Gets or sets the block diagonal eigenvalue matrix.

#### TDeterminant get;

Gets the absolute value of determinant of the square matrix for which the EVD was computed.

#### Vector<T>EigenValues get;

Gets or sets the eigen values (λ) of matrix in ascending value.

#### Matrix<T>EigenVectors get;

Gets or sets eigenvectors.

#### boolIsFullRank get;

Gets a value indicating whether the matrix is full rank or not.
Value:

#### boolIsSymmetric get;

Gets or sets a value indicating whether matrix is symmetric or not

#### intRank get;

Gets the effective numerical matrix rank.
Value: